Finite Group Databasebeta

← #34069430

Subgroups — #34069430

Order 19328.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012713C211yesmaximal, characteristic
2C2×#18012698C211yesmaximal, characteristic, complemented
3C2×#18012661C212yesmaximal, complemented
4#23751975C212yesmaximal, complemented
5C2×C22⋊C8×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7C22×C22⋊D151—21no—
8#18012713—22no—
9#18012713C414yescomplemented
10#18012698—24no—
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2212yes—
13C2×C22⋊Dic151—21no—
14C2×(C2×D151)⋊C4—21no—
15C2×C4×Dic151—21no—
16#18012661—24no—
17C23×C4×C151C2211yescharacteristic
18C22×C8×C151C2212yes—
19C22⋊C8×C151—22no—
20C23×D151—21no—
21C2×D604—22no—
22C2×D604—21no—
23C2×D604—22no—
24C2×D604C2×C412yes—
25C2×C22⋊D151—24no—
26C2×C22⋊D151—44no—
27C22×Dic151—22no—
28C22×Dic151—21no—
29C4⋊Dic151—22no—
30C4⋊Dic151—21no—
31C4⋊Dic151C2×C412yes—
32C4⋊Dic151D414yescomplemented
33C22⋊Dic151—24no—
34(C2×D151)⋊C4—24no—
35C4×Dic151—24no—
36C24×C151D411yescharacteristic
37C22×C4×C151—22no—
38C22×C4×C151—22no—
39C22×C4×C151C2×C412yes—
40C22×C4×C151D412yes—
41C22×C4×C151D411yescharacteristic
42C22×C4×C151C2311yescharacteristic
43C2×C8×C151—22no—
44C2×C8×C151—22no—
45C2×C8×C151—22no—
46C22×D151—22no—
47C22×D151—41no—
48C22×D151—41no—
49C22×D151—42no—
50C22×D151—42no—
51D604—24no—
52D604—42no—
53C22⋊D151—48no—
54C2×Dic151—22no—
55C2×Dic151—24no—
56C2×Dic151—42no—
57C2×Dic151—42no—
58C2×Dic151—42no—
59C23×C151—21no—
60C23×C151—21no—
61C23×C151—22no—
62C23×C151—22no—
63C23×C151C22⋊C412yes—
64C23×C151C2×D411yescharacteristic
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—24no—
68C2×C4×C151—24no—
69C2×C4×C151C22⋊C412yes—
70C2×C4×C151C22×C411yescharacteristic
71C2×C4×C151C2×D412yes—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151#4112yes—
74C8×C151—42no—
75C22×C151—22no—
76C22×C151—22no—
77C22×C151—22no—
78C22×C151—42no—
79C22×C151—42no—
80C22×C151C2×C22⋊C411yescharacteristic
81C22×C151#12011yescharacteristic
82C22×C151#12311yescharacteristic
83C22×C151#13512yes—
84C22×C151AGL(1,ℤ/8)12yes—
85C2×D151—42no—
86C2×D151—42no—
87C2×D151—42no—
88C2×D151—82no—
89C2×D151—82no—
90C4×C151—22no—
91C4×C151C4×D412yes—
92C4×C151#12112yes—
93Dic151—42no—
94Dic151—44no—
95C2×C151—42no—
96C2×C151#38611yescharacteristic
97C2×C151#41611yescharacteristic
98C2×C151#41811yescharacteristic
99C2×C151#44912yes—
100C2×C151#48212yes—
101D151—82no—
102C151#187511yescharacteristic, complemented, Sylow
103#1875—1511nomaximal, Sylow
104C2×#121—1511no—
105C2×#117—1511no—
106C2×#102—1512no—
107C2×C22⋊C8D15111yescharacteristic, complemented
108#340—1512no—
109C22×D4—3021no—
110C22×D4—1511no—
111C23×C4C2×D15111yescharacteristic
112C22×C8C2×D15112yes—
113#121—3022no—
114#121—1514no—
115#117—3024no—
116C2×C4⋊C4—1512no—
117C2×C4⋊C4—1511no—
118C2×C22⋊C4—3021no—
119C2×C22⋊C4—3021no—
120C2×C42—3021no—
121#102—3024no—
122C22⋊C8—22no—
123C24—3021no—
124C24D60411yescharacteristic
125C2×D4—3024no—
126C2×D4—3022no—
127C2×D4—3021no—
128C2×D4—3022no—
129C2×D4—6044no—
130C2×D4—1512no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—3022no—
134C22×C4—3021no—
135C22×C4C4×D15112yes—
136C22×C4C22⋊D15112yes—
137C22×C4D60411yescharacteristic
138C22×C4C22×D15111yescharacteristic
139C2×C8—22no—
140C2×C8—22no—
141C2×C8—22no—
142C4⋊C4—3022no—
143C4⋊C4—3021no—
144C4⋊C4—1512no—
145C4⋊C4—1514no—
146C22⋊C4—3024no—
147C22⋊C4—3024no—
148C42—3024no—
149C23—21no—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—3022no—
154C23—6041no—
155C23—6041no—
156C23—6042no—
157C23—6042no—
158C23(C2×D151)⋊C412yes—
159C23C2×D60411yescharacteristic
160D4—3024no—
161D4—6048no—
162D4—6042no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—3022no—
168C2×C4—3024no—
169C2×C4—6042no—
170C2×C4—6042no—
171C2×C4—6042no—
172C2×C4(C2×D151)⋊C412yes—
173C2×C4C2×C4×D15111yescharacteristic
174C2×C4D4×D15112yes—
175C2×C4C2×C22⋊D15111yescharacteristic
176C2×C4#1455900312yes—
177C8—42no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—6042no—
184C22—6042no—
185C22—6042no—
186C22—12082no—
187C22—12082no—
188C22C2×(C2×D151)⋊C411yescharacteristic
189C22#1801270911yescharacteristic
190C22#1801272311yescharacteristic
191C22#1801276112yes—
192C22#1801276712yes—
193C4—22no—
194C4—6042no—
195C4—6044no—
196C4(C22⋊D151)⋊C412yes—
197C4#1801271112yes—
198C2—42no—
199C2—12082no—
200C2#2375208911yescharacteristic
201C2#2375220911yescharacteristic
202C2#2375221811yescharacteristic
203C2#2375235912yes—
204C2#2375253712yes—
subgroupG/H
centerC23C2×D604
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC2×C22⋊C8×C151C2
socleC23×C151C2×D4
prime radicalC2×#18012713C2
cosocleC22×C4×C151C23
hypercenterC2×C22⋊C8D151
hypocenterC151#1875
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#18012698C2semidirect
3. C2×#18012661C2semidirect
4. #23751975C2semidirect
5. C2×C22⋊C8×C151C2semidirect
9. #18012713C4semidirect
32. C4⋊Dic151D4semidirect
102. C151#1875semidirect
107. C2×C22⋊C8D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180127132
C2×#180126982
C2×#180126612
#237519752
C2×C22⋊C8×C1512
#1875151